Triangulation from Two Views Revisited: Hartley-Sturm vs. Optimal Correction

Kanatani, Kenichi; Sugaya, Yasuyuki; Niitsuma, Hirotaka

doi:10.5244/c.22.18

Cited by 81 publications

(66 citation statements)

References 9 publications

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“…It is used to measure the degree by which F deviates from satisfying the singularity constraint. The reprojection error of a given correspondence M M M i with respect to F was measured by first correcting M M M i intoM M M i with Kanatani's iterative correction [13] and measuring the distance between M M M i andM M M i .…”

Section: Resultsmentioning

confidence: 99%

Simple, Fast and Accurate Estimation of the Fundamental Matrix Using the Extended Eight-Point Schemes

Fathy

Hussein

Tolba

2010

Procedings of the British Machine Vision Conference 2010

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The eight-point scheme is the simplest and fastest scheme for estimating the fundamental matrix (FM) from a number of noisy correspondences. As it ignores the fact that the FM must be singular, the resulting FM estimate is often inaccurate. Existing schemes that take the singularity constraint into consideration are several times slower and significantly more difficult to implement and understand. This paper describes extended versions of the eight-point (8P) and the weighted eight-point (W8P) schemes that effectively take the singularity constraint into consideration without sacrificing the efficiency and the simplicity of both schemes. The proposed schemes are respectively called the extended eight-point scheme (E8P) and the extended weighted eight-point scheme (EW8P). The E8P scheme was experimentally found to give exactly the same results as Hartley's algebraic distance minimization scheme while being almost as fast as the simplest scheme (i.e., the 8P scheme). At the expense of extra calculations per iteration, the EW8P scheme permits the use of geometric cost functions and, more importantly, robust weighting functions. It was experimentally found to give near-optimal results while being 8-16 times faster than the more complicated schemes such as Levenberg-Marquardt schemes. The FM estimates obtained by the E8P and the EW8P schemes perfectly satisfy the singularity constraint, eliminating the need to enforce the rank-2 constraint in a post-processing step.

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Section: Resultsmentioning

confidence: 99%

Simple, Fast and Accurate Estimation of the Fundamental Matrix Using the Extended Eight-Point Schemes

Fathy

Hussein

Tolba

2010

Procedings of the British Machine Vision Conference 2010

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“…In order to evaluate a given fundamental matrix F and a set of n matches (x i , x ′ i ) 1≤i≤n we use the implementation of Kanatani [8] 8 to compute the optimal matches for the given data; we use as measure the RMSE of the reprojection error associated to these optimal matches.…”

Section: Optimal Reprojection Errormentioning

confidence: 99%

A New A Contrario Approach for the Robust Determination of the Fundamental Matrix

Espuny

Monasse

Moisan

2014

Image and Video Technology – PSIVT 2013 Workshops

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Abstract. The fundamental matrix is a two-view tensor that plays a central role in Computer Vision geometry. We address its robust estimation given correspondences between image features. We use a nonparametric estimate of the distribution of image features, and then follow a probabilistic approach to select the best possible set of inliers among the given feature correspondences. The use of this perception-based a contrario principle allows us to avoid the selection of a precision threshold as in RANSAC, since we provide a decision criterion that integrates all data and method parameters (total number of points, precision threshold, number of inliers given this threshold). Our proposal is analyzed in simulated and real data experiments; it yields a significant improvement of the ORSA method proposed in 2004, in terms of reprojection error and relative motion estimation, especially in situations of low inlier ratios.

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“…We added independent Gaussian noise of mean 0 and standard deviation σ pixels to the x and y coordinates of each of the grid points in these images and computed their 3-D positionsr α andr α by the method described in [15]. For optimal similarity estimation, we need to evaluate the normalized covariances V 0 [r α ] and V 0 [r α ] of the reconstructed 3-D positionsr α and r α .…”

Section: Covariance Evaluationmentioning

confidence: 99%

Optimal computation of 3-D similarity: Gauss–Newton vs. Gauss–Helmert

Kanatani

Niitsuma

2012

Computational Statistics & Data Analysis

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Because 3-D data are acquired using 3-D sensing such as stereo vision and laser range finders, they have inhomogeneous and anisotropic noise. This paper studies optimal computation of the similarity (rotation, translation, and scale change) of such 3-D data. We first point out that the Gauss-Newton and the Gauss-Helmert methods, regarded as different techniques, have similar structures. We then combine them to define what we call the modified Gauss-Helmert method and do stereo vision simulation to show that it is superior to either of the two in convergence performance. Finally, we show an application to real GPS geodetic data and point out that the widely used homogeneous and isotropic noise model is insufficient and that GPS geodetic data are prone to numerical problems.

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Triangulation from Two Views Revisited: Hartley-Sturm vs. Optimal Correction

Cited by 81 publications

References 9 publications

Simple, Fast and Accurate Estimation of the Fundamental Matrix Using the Extended Eight-Point Schemes

Simple, Fast and Accurate Estimation of the Fundamental Matrix Using the Extended Eight-Point Schemes

A New A Contrario Approach for the Robust Determination of the Fundamental Matrix

Optimal computation of 3-D similarity: Gauss–Newton vs. Gauss–Helmert

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